How do I find the value of k to make the equations of a line and a plane be parallel?

Question

Given the equation of the line $r$:

$r:\frac{x-2}{k}=\frac{y-1}{2}=z$

And the equation of the plane $\alpha$:

$\alpha:3x-ky-z-2=0$

How do I determine $k$ such that the line $r$ and the plane $\alpha$ are parallel?

Answer 1

Thanks guys, @Vectorizer and @Math Lover

So, by the equation of $\alpha$, I know that the normal vector is $(3, - k, - 1)$ and from the equation of $r$, I know that it's director vector is $(k, 2, 1)$

With that said, the dot product of both have to be $=0$, and so:

$3k-2k-1=0 \Leftrightarrow k=1$

I have to study harder!!